Title: A single theory for some quasi-static, supersonic, atomic, and tectonic scale applications of dislocations

I will describe a PDE model that reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. As applications, we explore the existence of a Peierls stress in a continuum theory, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-à-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics.